$\"\"$

\

Determine whether the given function is linear or non-linear.

\

First compute the average rate of change of $\"\"$ with respect to $\"\"$ and then compute the ratio of the consecutive outputs.

\

If the average rate of change is constant, then the function is linear else non-linear.

\ \

\ \ \ \ \ \ \ \ \ \

\"\"

\"\"

Average rate of change

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$ $\"\"$

\

$\"\"$

\

$\"\"$ $\"\"$

\

\

$\"\"$

\

Observe the table.

\

For the given function, the average rate of change is $\"\"$ .

\

Since the average rate of change is constant , the function is a linear function.

\

Definition of the slope :

\

If the average rate of change of the function is constant then slope of the line is the average rate of change of the function.

\

Slope of the linear function is $\"\"$ .

\

$\"\"$

\

The function is linear.

\

Slope of the linear function is $\"\"$ .